Problem: Rewrite as a simplified fraction. ${0.\overline{80} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}100x &= 80.808...\\ 1x &= 0.808...\end{aligned}}$ Subtracting the two equations, we have: ${99x = 80}$ ${x = \dfrac{80}{99}} $